Pointed Drawings of Planar Graphs

We study the problem how to draw a planar graph such that every vertex is incident to an angle greater than π. In general a straightline embedding cannot guarantee this property. We present algorithms which construct such drawings with either tangent-continuous biarcs or quadratic B´ezier curves (parabolic arcs), even if the positions of the vertices are predefined by a given plane straight-line embedding of the graph. Moreover, the graph can be embedded with circular arcs if the vertices can be placed arbitrarily. The topic is related to non-crossing drawings of multigraphs and vertex labeling.

• Type: Conference
• Year: 2007
• Where: CCCG
• Authors: Oswin Aichholzer, Günter Rote, André Schulz, Birgit Vogtenhuber
• Keywords: CCCG 2007, Computational Geometry, Planar Graph, Plane Straight-line Embedding, Straightline Embedding